Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval.

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• Existing bivariate beta distributions have limitations.
• There is a need for more flexible and generalizable bivariate distributions.
• Univariate Kummer-beta distributions serve as a basis for generalization.

Purpose of the Study:

• To propose a novel generalized bivariate Kummer-beta distribution.
• To derive key statistical properties of this new distribution.
• To explore its potential applications and parameter estimation methods.

Main Methods:

• Derivation of product moments, marginal and conditional densities/moments.
• Calculation of Rényi and Shannon entropy.
• Development of parameter estimation using maximum likelihood.
• Conducting a simulation study for finite sample inference.

Main Results:

• The proposed distribution generalizes several existing bivariate beta distributions.
• Key properties including moments, entropies, and conditional distributions are derived.
• Maximum likelihood estimators are formulated, and their finite sample performance is assessed.

Conclusions:

• The generalized bivariate Kummer-beta distribution offers a flexible framework for statistical modeling.
• The derived properties and estimation methods support its practical application.
• Simulation results validate the theoretical findings for parameter estimation.